Subgroups — C₁₃×#61285 #15747624

Order 3328.

1818 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3351	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3340	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3337	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3097	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3096	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2912	C₂	1	2	yes	maximal, complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#131	C₂²	1	2	yes	—
20	C₁₃×#559	—	2	1	no	—
21	C₁₃×#559	—	2	2	no	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	—	2	2	no	—
25	C₁₃×#556	C₂²	1	2	yes	complemented
26	C₁₃×#555	C₂²	1	2	yes	—
27	C₁₃×#554	C₂²	1	2	yes	complemented
28	C₁₃×#553	C₂²	1	4	yes	—
29	C₁₃×#552	C₂²	1	4	yes	complemented
30	C₁₃×#550	—	2	1	no	—
31	C₁₃×#547	C₂²	1	2	yes	—
32	C₁₃×#539	—	2	2	no	—
33	C₁₃×#538	—	2	2	no	—
34	C₁₃×#536	C₂²	1	2	yes	—
35	C₁₃×#535	C₂²	1	2	yes	—
36	C₁₃×#533	C₂²	1	1	yes	characteristic
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#532	C₂²	1	1	yes	characteristic
39	C₁₃×#529	—	2	2	no	—
40	C₁₃×#525	—	2	2	no	—
41	C₁₃×#520	C₂²	1	2	yes	—
42	C₁₃×#520	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#499	C₂²	1	2	yes	complemented
48	C₁₃×#499	C₂²	1	2	yes	complemented
49	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#485	C₂²	1	4	yes	complemented
52	C₁₃×#485	C₂²	1	4	yes	complemented
53	C₁₃×#484	C₂²	1	4	yes	complemented
54	C₁₃×#483	C₂²	1	4	yes	complemented
55	C₁₃×#482	C₂²	1	4	yes	—
56	C₁₃×#482	C₂²	1	4	yes	—
57	C₁₃×#481	C₂²	1	4	yes	—
58	C₁₃×#480	C₂²	1	4	yes	—
59	C₁₃×#479	C₂²	1	4	yes	complemented
60	C₁₃×#478	C₂²	1	4	yes	—
61	C₁₃×#477	C₂²	1	2	yes	complemented
62	C₁₃×#476	C₂²	1	2	yes	—
63	C₁₃×#475	C₂²	1	2	yes	complemented
64	C₁₃×#474	C₂²	1	2	yes	—
65	C₁₃×#468	C₂²	1	4	yes	—
66	C₁₃×#468	C₂²	1	4	yes	—
67	C₁₃×#465	C₂²	1	4	yes	—
68	C₁₃×#465	C₂²	1	4	yes	—
69	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
70	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
71	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
72	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
73	C₁₃×#436	C₂²	1	2	yes	complemented
74	C₁₃×#436	C₂²	1	2	yes	complemented
75	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
76	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
77	C₁₃×#428	C₂²	1	2	yes	—
78	C₁₃×#428	C₂²	1	2	yes	—
79	C₁₃×#428	C₂²	1	4	yes	complemented
80	C₁₃×#428	C₂²	1	4	yes	complemented
81	C₁₃×#427	C₂²	1	2	yes	—
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#427	C₂²	1	4	yes	complemented
84	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
85	C₂×C₁₃×#106	C₂²	1	4	yes	complemented
86	C₁₃×#423	C₂²	1	1	yes	characteristic
87	C₁₃×#419	C₂²	1	2	yes	—
88	C₁₃×#418	C₂²	1	2	yes	—
89	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
91	C₁₃×#408	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	—	2	2	no	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂×C₁₃×SD₁₆	—	2	4	no	—
99	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
101	C₁₃×#131	—	2	8	no	—
102	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
103	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
106	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
109	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×#127	—	2	2	no	—
114	C₁₃×#127	D₄	1	1	yes	characteristic
115	C₁₃×#126	—	2	4	no	—
116	C₁₃×#126	—	2	4	no	—
117	C₁₃×#126	—	2	4	no	—
118	C₁₃×#125	—	2	2	no	—
119	C₁₃×#125	—	2	4	no	—
120	C₁₃×#125	C₂³	1	2	yes	—
121	C₁₃×#125	C₂³	1	2	yes	—
122	C₁₃×#124	—	2	2	no	—
123	C₁₃×#124	—	2	2	no	—
124	C₁₃×#124	—	2	2	no	—
125	C₁₃×#124	—	2	4	no	—
126	C₁₃×#124	D₄	1	2	yes	—
127	C₁₃×#123	—	2	4	no	—
128	C₁₃×#123	—	2	4	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×#123	—	2	4	no	—
131	C₁₃×C₂²⋊Q₈	—	2	1	no	—
132	C₁₃×C₂²⋊Q₈	—	2	1	no	—
133	C₁₃×C₂²⋊Q₈	—	2	1	no	—
134	C₁₃×C₂²⋊Q₈	—	2	1	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	4	no	—
137	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
138	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
139	C₁₃×#121	—	2	2	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	D₄	1	2	yes	—
142	C₁₃×#121	D₄	1	2	yes	—
143	C₁₃×#121	C₂³	1	4	yes	—
144	C₁₃×#121	C₂³	1	4	yes	—
145	C₁₃×#120	—	2	4	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	1	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	4	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	2	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₄×D₄×C₁₃	—	2	1	no	—
164	C₄×D₄×C₁₃	—	2	1	no	—
165	C₄×D₄×C₁₃	C₂³	1	2	yes	—
166	C₄×D₄×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	C₂³	1	2	yes	—
168	C₄×D₄×C₁₃	C₂³	1	2	yes	—
169	C₁₃×#117	—	2	2	no	—
170	C₁₃×#117	—	2	4	no	—
171	C₁₃×#117	C₂³	1	2	yes	—
172	C₁₃×#117	C₂³	1	2	yes	—
173	C₁₃×#117	C₂³	1	4	yes	—
174	C₁₃×#117	C₂³	1	4	yes	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
180	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
181	C₂×C₄²×C₁₃	—	2	1	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	2	yes	—
185	C₁₃×#107	C₂³	1	2	yes	—
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#107	C₂³	1	4	yes	—
188	C₁₃×#107	C₂³	1	4	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×#106	C₂³	1	4	yes	—
193	C₁₃×#106	C₂³	1	4	yes	—
194	C₁₃×#106	C₂³	1	2	yes	—
195	C₁₃×#106	C₂³	1	2	yes	—
196	C₁₃×#106	C₂³	1	2	yes	—
197	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
198	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#103	C₂³	1	4	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	4	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
213	#61285	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂⁴×C₁₃	—	2	1	no	—
215	C₁₃×#41	—	2	4	no	—
216	C₁₃×#41	—	2	4	no	—
217	C₁₃×#41	—	8	4	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	1	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	1	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	—	2	4	no	—
228	C₂×D₄×C₁₃	—	2	4	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	—	2	4	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	2	2	no	—
244	C₂²×C₄×C₁₃	—	8	2	no	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₁₃×SD₁₆	—	2	4	no	—
250	C₁₃×SD₁₆	—	2	4	no	—
251	C₁₃×M₁₆	—	2	4	no	—
252	C₁₃×M₁₆	—	2	8	no	—
253	C₂×C₈×C₁₃	—	2	2	no	—
254	C₂×C₈×C₁₃	—	2	8	no	—
255	C₂×C₈×C₁₃	#41	1	4	yes	complemented
256	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
259	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	2	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	2	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	2	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	2	no	—
273	C₁₃×C₄⋊C₄	—	2	1	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	1	no	—
276	C₁₃×C₄⋊C₄	—	2	4	no	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₂²⋊C₄	—	2	4	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	4	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	2	no	—
292	C₁₃×C₂²⋊C₄	—	2	2	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	4	no	—
295	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
296	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	2	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	2	no	—
302	C₄²×C₁₃	—	2	2	no	—
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
307	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#3506	C₂×C₁₃	1	1	yes	characteristic
309	#3357	C₂×C₁₃	1	2	yes	complemented
310	#3353	C₂×C₁₃	1	2	yes	complemented
311	#3351	C₂×C₁₃	1	4	yes	complemented
312	#3340	C₂×C₁₃	1	2	yes	complemented
313	#3337	C₂×C₁₃	1	4	yes	complemented
314	#3335	C₂×C₁₃	1	2	yes	complemented
315	#3160	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#3097	C₂×C₁₃	1	2	yes	complemented
317	#3096	C₂×C₁₃	1	2	yes	complemented
318	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#3077	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#3057	C₂×C₁₃	1	2	yes	complemented
321	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2912	C₂×C₁₃	1	2	yes	complemented
324	C₂³×C₁₃	—	2	2	no	—
325	C₂³×C₁₃	—	4	2	no	—
326	C₂³×C₁₃	—	8	1	no	—
327	C₂³×C₁₃	—	8	1	no	—
328	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
329	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
330	Q₈×C₁₃	—	2	4	no	—
331	Q₈×C₁₃	—	2	2	no	—
332	Q₈×C₁₃	—	2	2	no	—
333	Q₈×C₁₃	—	4	2	no	—
334	Q₈×C₁₃	—	4	2	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	8	1	no	—
337	Q₈×C₁₃	—	8	1	no	—
338	D₄×C₁₃	—	2	8	no	—
339	D₄×C₁₃	—	2	4	no	—
340	D₄×C₁₃	—	2	4	no	—
341	D₄×C₁₃	—	2	2	no	—
342	D₄×C₁₃	—	2	2	no	—
343	D₄×C₁₃	—	4	2	no	—
344	D₄×C₁₃	—	4	2	no	—
345	D₄×C₁₃	—	8	4	no	—
346	D₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	4	no	—
349	C₂×C₄×C₁₃	—	2	4	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	2	no	—
355	C₂×C₄×C₁₃	—	2	2	no	—
356	C₂×C₄×C₁₃	—	2	2	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	4	4	no	—
360	C₂×C₄×C₁₃	—	8	2	no	—
361	C₂×C₄×C₁₃	—	8	1	no	—
362	C₂×C₄×C₁₃	—	8	4	no	—
363	C₂×C₄×C₁₃	—	8	1	no	—
364	C₂×C₄×C₁₃	—	8	4	no	—
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
367	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
372	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
373	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
374	C₈×C₁₃	—	2	4	no	—
375	C₈×C₁₃	—	2	1	no	—
376	C₈×C₁₃	—	2	1	no	—
377	C₈×C₁₃	C₂×#41	1	2	yes	—
378	C₈×C₁₃	C₂×#41	1	2	yes	—
379	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#131	C₂²×C₁₃	1	2	yes	—
381	#559	—	2	1	no	—
382	#559	—	2	2	no	—
383	#557	—	2	1	no	—
384	#556	—	2	1	no	—
385	#556	—	2	2	no	—
386	#556	C₂²×C₁₃	1	2	yes	complemented
387	#555	C₂²×C₁₃	1	2	yes	—
388	#554	C₂²×C₁₃	1	2	yes	complemented
389	#553	C₂²×C₁₃	1	4	yes	—
390	#552	C₂²×C₁₃	1	4	yes	complemented
391	#550	—	2	1	no	—
392	#547	C₂²×C₁₃	1	2	yes	—
393	#539	—	2	2	no	—
394	#538	—	2	2	no	—
395	#536	C₂²×C₁₃	1	2	yes	—
396	#535	C₂²×C₁₃	1	2	yes	—
397	#533	C₂²×C₁₃	1	1	yes	characteristic
398	#533	C₂²×C₁₃	1	1	yes	characteristic
399	#532	C₂²×C₁₃	1	1	yes	characteristic
400	#529	—	2	2	no	—
401	#525	—	2	2	no	—
402	#520	C₂²×C₁₃	1	2	yes	—
403	#520	C₂²×C₁₃	1	2	yes	—
404	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
406	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	#499	C₂²×C₁₃	1	2	yes	complemented
409	#499	C₂²×C₁₃	1	2	yes	complemented
410	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	#485	C₂²×C₁₃	1	4	yes	complemented
413	#485	C₂²×C₁₃	1	4	yes	complemented
414	#484	C₂²×C₁₃	1	4	yes	complemented
415	#483	C₂²×C₁₃	1	4	yes	complemented
416	#482	C₂²×C₁₃	1	4	yes	—
417	#482	C₂²×C₁₃	1	4	yes	—
418	#481	C₂²×C₁₃	1	4	yes	—
419	#480	C₂²×C₁₃	1	4	yes	—
420	#479	C₂²×C₁₃	1	4	yes	complemented
421	#478	C₂²×C₁₃	1	4	yes	—
422	#477	C₂²×C₁₃	1	2	yes	complemented
423	#476	C₂²×C₁₃	1	2	yes	—
424	#475	C₂²×C₁₃	1	2	yes	complemented
425	#474	C₂²×C₁₃	1	2	yes	—
426	#468	C₂²×C₁₃	1	4	yes	—
427	#468	C₂²×C₁₃	1	4	yes	—
428	#465	C₂²×C₁₃	1	4	yes	—
429	#465	C₂²×C₁₃	1	4	yes	—
430	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
431	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
432	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
433	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
434	#436	C₂²×C₁₃	1	2	yes	complemented
435	#436	C₂²×C₁₃	1	2	yes	complemented
436	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
437	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
438	#428	C₂²×C₁₃	1	2	yes	—
439	#428	C₂²×C₁₃	1	2	yes	—
440	#428	C₂²×C₁₃	1	4	yes	complemented
441	#428	C₂²×C₁₃	1	4	yes	complemented
442	#427	C₂²×C₁₃	1	2	yes	—
443	#427	C₂²×C₁₃	1	2	yes	—
444	#427	C₂²×C₁₃	1	4	yes	complemented
445	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×#106	C₂²×C₁₃	1	4	yes	complemented
447	#423	C₂²×C₁₃	1	1	yes	characteristic
448	#419	C₂²×C₁₃	1	2	yes	—
449	#418	C₂²×C₁₃	1	2	yes	—
450	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
452	#408	C₂²×C₁₃	1	2	yes	—
453	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
454	C₂²×C₁₃	—	2	1	no	—
455	C₂²×C₁₃	—	2	1	no	—
456	C₂²×C₁₃	—	2	4	no	—
457	C₂²×C₁₃	—	2	4	no	—
458	C₂²×C₁₃	—	2	4	no	—
459	C₂²×C₁₃	—	4	2	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	4	2	no	—
462	C₂²×C₁₃	—	8	4	no	—
463	C₂²×C₁₃	#547	1	2	yes	—
464	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₁₃	—	2	1	no	—
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	4	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	4	2	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	#547	1	2	yes	—
477	C₄×C₁₃	#577	1	2	yes	—
478	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
479	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
480	C₂×#41	—	2	2	no	—
481	C₂×#41	C₂³×C₁₃	1	2	yes	—
482	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂³×C₄	—	2	1	no	—
485	C₂×SD₁₆	—	2	4	no	—
486	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
487	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
488	#131	—	2	8	no	—
489	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
490	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
491	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
492	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
496	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
497	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
500	#127	—	2	2	no	—
501	#127	D₄×C₁₃	1	1	yes	characteristic
502	#126	—	2	4	no	—
503	#126	—	2	4	no	—
504	#126	—	2	4	no	—
505	#125	—	2	2	no	—
506	#125	—	2	4	no	—
507	#125	C₂³×C₁₃	1	2	yes	—
508	#125	C₂³×C₁₃	1	2	yes	—
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	—	2	4	no	—
513	#124	D₄×C₁₃	1	2	yes	—
514	#123	—	2	4	no	—
515	#123	—	2	4	no	—
516	#123	—	2	4	no	—
517	#123	—	2	4	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	1	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	4	no	—
524	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
525	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
526	#121	—	2	2	no	—
527	#121	—	2	4	no	—
528	#121	D₄×C₁₃	1	2	yes	—
529	#121	D₄×C₁₃	1	2	yes	—
530	#121	C₂³×C₁₃	1	4	yes	—
531	#121	C₂³×C₁₃	1	4	yes	—
532	#120	—	2	4	no	—
533	C₄×Q₈	—	2	2	no	—
534	C₄×Q₈	—	2	2	no	—
535	C₄×Q₈	—	2	2	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
543	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
544	C₄×D₄	—	2	4	no	—
545	C₄×D₄	—	2	4	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	4	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	C₂³×C₁₃	1	2	yes	—
553	C₄×D₄	C₂³×C₁₃	1	2	yes	—
554	C₄×D₄	C₂³×C₁₃	1	2	yes	—
555	C₄×D₄	C₂³×C₁₃	1	2	yes	—
556	#117	—	2	2	no	—
557	#117	—	2	4	no	—
558	#117	C₂³×C₁₃	1	2	yes	—
559	#117	C₂³×C₁₃	1	2	yes	—
560	#117	C₂³×C₁₃	1	4	yes	—
561	#117	C₂³×C₁₃	1	4	yes	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
566	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₄²	—	2	1	no	—
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	#107	C₂³×C₁₃	1	2	yes	—
571	#107	C₂³×C₁₃	1	2	yes	—
572	#107	C₂³×C₁₃	1	2	yes	—
573	#107	C₂³×C₁₃	1	2	yes	—
574	#107	C₂³×C₁₃	1	4	yes	—
575	#107	C₂³×C₁₃	1	4	yes	—
576	#106	C₂³×C₁₃	1	2	yes	—
577	#106	C₂³×C₁₃	1	2	yes	—
578	#106	C₂³×C₁₃	1	2	yes	—
579	#106	C₂³×C₁₃	1	4	yes	—
580	#106	C₂³×C₁₃	1	4	yes	—
581	#106	C₂³×C₁₃	1	2	yes	—
582	#106	C₂³×C₁₃	1	2	yes	—
583	#106	C₂³×C₁₃	1	2	yes	—
584	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
585	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
586	#103	C₂³×C₁₃	1	2	yes	—
587	#103	C₂³×C₁₃	1	2	yes	—
588	#103	C₂³×C₁₃	1	4	yes	—
589	#103	C₂³×C₁₃	1	4	yes	—
590	#102	C₂³×C₁₃	1	2	yes	—
591	#102	C₂³×C₁₃	1	2	yes	—
592	#102	C₂³×C₁₃	1	4	yes	—
593	#102	C₂³×C₁₃	1	4	yes	—
594	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
595	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
596	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
600	C₂×C₁₃	—	2	2	no	—
601	C₂×C₁₃	—	4	4	no	—
602	C₂×C₁₃	—	8	2	no	—
603	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
604	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
605	C₂×C₁₃	#3584	1	1	yes	characteristic
606	C₂⁴	—	2	1	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	8	4	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	2	no	—
616	C₂×Q₈	—	2	2	no	—
617	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
618	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	2	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
625	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
626	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
627	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
628	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	8	2	no	—
637	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
641	SD₁₆	—	2	4	no	—
642	SD₁₆	—	2	4	no	—
643	M₁₆	—	2	4	no	—
644	M₁₆	—	2	8	no	—
645	C₂×C₈	—	2	2	no	—
646	C₂×C₈	—	2	8	no	—
647	C₂×C₈	C₁₃×#41	1	4	yes	complemented
648	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
649	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
650	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
651	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
652	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
671	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
673	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
675	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
676	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
688	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	2	no	—
694	C₄²	—	2	2	no	—
695	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
697	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
699	C₁₃	#61285	1	1	yes	characteristic, direct product factor, Sylow
700	C₂³	—	2	2	no	—
701	C₂³	—	4	2	no	—
702	C₂³	—	8	1	no	—
703	C₂³	—	8	1	no	—
704	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
705	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
706	Q₈	—	2	4	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	4	2	no	—
710	Q₈	—	4	2	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	1	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	8	no	—
715	D₄	—	2	4	no	—
716	D₄	—	2	4	no	—
717	D₄	—	2	2	no	—
718	D₄	—	2	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	4	2	no	—
721	D₄	—	8	4	no	—
722	D₄	—	8	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	4	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	8	2	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	4	no	—
740	C₂×C₄	—	8	4	no	—
741	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
745	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
746	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
747	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
748	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
749	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
750	C₈	—	2	4	no	—
751	C₈	—	2	1	no	—
752	C₈	—	2	1	no	—
753	C₈	C₂×C₁₃×#41	1	2	yes	—
754	C₈	C₂×C₁₃×#41	1	2	yes	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	4	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	8	4	no	—
764	C₂²	C₁₃×#547	1	2	yes	—
765	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	4	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₁₃×#547	1	2	yes	—
778	C₄	C₁₃×#577	1	2	yes	—
779	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
780	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
781	C₂	—	2	2	no	—
782	C₂	—	4	4	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
785	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
786	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3357	C₂	semidirect
4. C₁₃×#3353	C₂	semidirect
5. C₁₃×#3351	C₂	semidirect
6. C₁₃×#3340	C₂	semidirect
7. C₁₃×#3337	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3160	C₂	semidirect
10. C₁₃×#3097	C₂	semidirect
11. C₁₃×#3096	C₂	semidirect
12. C₁₃×#3078	C₂	semidirect
13. C₁₃×#3077	C₂	semidirect
14. C₁₃×#3057	C₂	semidirect
15. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
16. C₁₃×#2931	C₂	semidirect
17. C₁₃×#2912	C₂	semidirect
25. C₁₃×#556	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
29. C₁₃×#552	C₂²	semidirect
45. C₁₃×#500	C₂²	semidirect
46. C₁₃×#500	C₂²	semidirect
47. C₁₃×#499	C₂²	semidirect
48. C₁₃×#499	C₂²	semidirect
49. C₁₃×#498	C₂²	semidirect
50. C₁₃×#498	C₂²	semidirect
51. C₁₃×#485	C₂²	semidirect
52. C₁₃×#485	C₂²	semidirect
53. C₁₃×#484	C₂²	semidirect
54. C₁₃×#483	C₂²	semidirect
59. C₁₃×#479	C₂²	semidirect
61. C₁₃×#477	C₂²	semidirect
63. C₁₃×#475	C₂²	semidirect
73. C₁₃×#436	C₂²	semidirect
74. C₁₃×#436	C₂²	semidirect
75. C₈×D₄×C₁₃	C₂²	semidirect
76. C₈×D₄×C₁₃	C₂²	semidirect
79. C₁₃×#428	C₂²	semidirect
80. C₁₃×#428	C₂²	semidirect
83. C₁₃×#427	C₂²	semidirect
85. C₂×C₁₃×#106	C₂²	semidirect
213. #61285	C₁₃	direct (N × H)
255. C₂×C₈×C₁₃	#41	semidirect
307. #3507	C₂×C₁₃	semidirect
309. #3357	C₂×C₁₃	semidirect
310. #3353	C₂×C₁₃	semidirect
311. #3351	C₂×C₁₃	semidirect
312. #3340	C₂×C₁₃	semidirect
313. #3337	C₂×C₁₃	semidirect
314. #3335	C₂×C₁₃	semidirect
315. #3160	C₂×C₁₃	semidirect
316. #3097	C₂×C₁₃	semidirect
317. #3096	C₂×C₁₃	semidirect
318. #3078	C₂×C₁₃	semidirect
319. #3077	C₂×C₁₃	semidirect
320. #3057	C₂×C₁₃	semidirect
321. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
322. #2931	C₂×C₁₃	semidirect
323. #2912	C₂×C₁₃	semidirect
386. #556	C₂²×C₁₃	semidirect
388. #554	C₂²×C₁₃	semidirect
390. #552	C₂²×C₁₃	semidirect
406. #500	C₂²×C₁₃	semidirect
407. #500	C₂²×C₁₃	semidirect
408. #499	C₂²×C₁₃	semidirect
409. #499	C₂²×C₁₃	semidirect
410. #498	C₂²×C₁₃	semidirect
411. #498	C₂²×C₁₃	semidirect
412. #485	C₂²×C₁₃	semidirect
413. #485	C₂²×C₁₃	semidirect
414. #484	C₂²×C₁₃	semidirect
415. #483	C₂²×C₁₃	semidirect
420. #479	C₂²×C₁₃	semidirect
422. #477	C₂²×C₁₃	semidirect
424. #475	C₂²×C₁₃	semidirect
434. #436	C₂²×C₁₃	semidirect
435. #436	C₂²×C₁₃	semidirect
436. C₈×D₄	C₂²×C₁₃	semidirect
437. C₈×D₄	C₂²×C₁₃	semidirect
440. #428	C₂²×C₁₃	semidirect
441. #428	C₂²×C₁₃	semidirect
444. #427	C₂²×C₁₃	semidirect
446. C₂×#106	C₂²×C₁₃	semidirect
647. C₂×C₈	C₁₃×#41	semidirect
699. C₁₃	#61285	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3507	2
C₁₃×#3506	2
C₁₃×#3357	2
C₁₃×#3353	2
C₁₃×#3351	2
C₁₃×#3340	2
C₁₃×#3337	2
C₁₃×#3335	2
C₁₃×#3160	2
C₁₃×#3097	2
C₁₃×#3096	2
C₁₃×#3078	2
C₁₃×#3077	2
C₁₃×#3057	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2931	2
C₁₃×#2912	2
#61285	13

Subgroups — C13×#61285 #15747624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61285 #15747624